Open Question
At what cold-reservoir temperature (in ℃) would a Carnot engine with a hot-reservoir temperature of 427℃ have an efficiency of 60%?
23. The Second Law of Thermodynamics
The Carnot Cycle
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A theoretical heat engine in space could operate between the Sun's 5500°C surface and the –270.3°C temperature of intergalactic space. What would be its maximum theoretical efficiency?
A
99.98%
B
95.1%
C
99.95%
Verified step by step guidance1
Convert the temperatures from Celsius to Kelvin. The temperature of the Sun's surface is 5500°C, which is 5500 + 273.15 = 5773.15 K. The temperature of intergalactic space is -270.3°C, which is -270.3 + 273.15 = 2.85 K.
Use the formula for the maximum efficiency of a heat engine, which is given by the Carnot efficiency: \( \eta = 1 - \frac{T_c}{T_h} \), where \( T_c \) is the cold reservoir temperature and \( T_h \) is the hot reservoir temperature.
Substitute the values into the Carnot efficiency formula: \( \eta = 1 - \frac{2.85}{5773.15} \).
Calculate the fraction \( \frac{2.85}{5773.15} \) to find the efficiency in decimal form.
Convert the efficiency from decimal form to percentage by multiplying by 100. This will give you the maximum theoretical efficiency of the heat engine.
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